Math CentralQuandaries & Queries


Question from Jacob, a student:

A valid UPC number , ABABABABAB- C must end in a 2 after using the rule:

3A +B+3A+B+3A+B+3A+B+3A+B+C=##2.

What would term C need to be in order to make the following UPC valid? 2741825293-C

Hi Jacob,

Apply the rule to the first 10 digits of the UPC which are 2741825293. Thus you get

\[3 \times 2 + 7 + 3 \times 4 \mbox{ and so on.}\]

What digit $C$ do you need to add to the result to obtain a three digit number with units digit 2?


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